VectorCalculus[Hessian] - computes the Hessian Matrix of a function from R^n to R

Calling Sequence

Hessian(f, v, det, opts)

Hessian(f, v=p, det, opts)

Parameters

f

-

algebraic expression

v

-

(optional) list(name); specify the variables of differentiation

p

-

(optional) list(algebraic); point at which the Hessian is evaluated

det

-

(optional); equation of the form determinant = true or false; specify whether to return the determinant (default: determinant = false)

opts

-

(optional) equation(s) of the form option=value; options passed on to the constructed Matrix

Description

•

The Hessian(f, v) command computes the Hessian Matrix of the function f with respect to the variables in v. This is the Matrix with an (i,j)th entry of diff(f, v[i], v[j]).

•

If v is not provided, the differentiation variables are determined from the ambient coordinate system (see SetCoordinates), if possible.

•

If p is supplied, the computed Hessian matrix will be evaluated at the corresponding point. The dimension of the point must equal the number of differentiation variables.

•

The det option specifies whether the determinant of the Hessian matrix is also returned. If given as determinant = true, or just determinant, then an expression sequence containing the Hessian matrix and its determinant is returned.

•

If any options are given in opts, they will be passed on to the construction of the returned Matrix. For details on available options, see Matrix.